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In this paper we present new theory and algorithms for 2-norm regression overthe max-plus semiring. As an application we also show how max-plus 2-normregression can be used in system identification of max-plus linear dynamicalsystems with Gaussian noise. We also introduce and provide methods for solvinga max-plus linear inverse problem with regularization, which can be used whenthe the original problem is not well posed.

Max-plus Linear Inverse Problems: 2-norm regression and system identification of max-plus linear dynamical systems with Gaussian noise